Members of Unison, GMB and Unite were due to take industrial action over pay but have announced they are postponing action in order to consult their members on a new pay offer.
Demonstrations were held across the country on July 10 over the 1% pay rise originally offered to local government workers.
Unison claims employees have seen their pay fall in value by 20% since 2010.
Lancaster City Council said all their services would be running as normal on Tuesday.